Winter was born near Wellington, Texas (a fact which later provided him with his nickname when his family moved to California) fifteen minutes after twin sister Mona Francis. The Winter family moved to Lubbock, Texas in 1929, where his mechanic father died of an infection then Tex was ten years old. Winter had to work while in elementary school to help his family, one such job was to collect boxes for a local baker in exchange for day-old bread. In 1936, Winter and his sister moved to Huntington Park, California with their mother, who would work as a clothing store sales manager. His older football star brother Ernest remained in Texas to finish high school while his older sister Elizabeth had already married and moved to California first and encouraged them to move there. While attending Huntington Park High School, Winter worked with Phil Woolpert and Pete Newell as a ball boy for Loyola University.

After graduation from high school in 1940, Winter attended college at Compton Community College in Los Angeles for two years, where he became a renowned pole vaulter and earned a scholarship to Oregon State University. He was on the basketball and track teams at both schools. As a pole vaulter, Winter competed against Bob Richards, a 1948 and 1952 olympian. He was considered a strong candidate for the US Olympic team in 1944, but the Olympics were cancelled by World War II.

Winter met his wife Nancy at Oregon State. Both of them entered the United States Navy in early 1943, with Winter going into fighter pilot training and his wife into WAVVES.[2] After his pilot's wings were conferred he was assigned to fighter pilot duty in the Pacific. However, his orders were rescinded after his brother's plane was shot down, and Winter remained at Naval Air Station Glenview in Illinois for the duration of the war. After the war, he was assigned to NAS Corpus Christi as a test pilot for an experimental jet craft. While in the navy, Winter was a starting guard for his basketball team under the commanding officer Chuck Taylor (salesman).[3] He left the Navy with the rank of Ensign in 1946.

In 1952, Winter began a two-year stint as head coach at Marquette University, becoming the youngest coach in major college basketball. In 1954 Winter returned to Kansas State.[4][5] Winter served as Kansas State's head coach for the following 15 years, posting a 261-118 (.689) record. He still owns the record for most league titles (eight) in school history and twice led the Wildcats to the Final Four (1958 and 1964). Winter guided K-State to postseason play seven times overall, including six trips to the NCAA Tournament, and boasts one of the highest winning percentages in K-State's history.

In 1962, Winter also wrote the book, entitled The Triple-Post Offense, on the triangle offense – the offense which he utilized with such success at Kansas State. Following his leaving Kansas State to his assistant Cotton Fitzsimmons, Winter served shorter stints as head coach at the University of Washington (where he was hired by then Athletic Director Joseph Kearney), Northwestern University, and Long Beach State. In 1982, LSU’s Dale Brown, who Winter befriended when Brown was a high school coach, hired him as an assistant for one year 1983-84.[6] In total, Winter won 454 games at the collegiate level.

Winter was hired by Pete Newell as head coach of the Houston Rockets for two seasons, 1971–1973, posting a 51-78 (.395) record.

In 1985, Winter started another chapter of his life after contemplating retirement, serving as an assistant coach with the Chicago Bulls, and teaching the triangle offense to Michael Jordan. He was hired to the position by General Manager Jerry Krause, an old friend he had met while at Kansas State. As an assistant to Phil Jackson, who took over as the Bulls' head coach in 1989, Winter and his triangle offense were an integral part of the Bulls' NBA championships in 1991, 1992, 1993, 1996, 1997, and 1998. Winter followed Phil Jackson to the Los Angeles Lakers, where he collected three additional championship rings, in 2000, 2001, and 2002. Winter was also a consultant for the NBA-champion 2008–09 Los Angeles Lakers team.[7]

On April 25, 2009, Winter suffered a stroke in Manhattan, Kansas, while attending a Kansas State basketball reunion.[8]

He lives in a yellow house near Kansas State in Manhattan, Kansas with his Alzheimer's-stricken wife[9] and son Brian. He still suffers from the after-effects of his 2009 stroke, counting an uncooperative right side and nerve pain in his neck and shoulder.[10] He has two other sons, Russ and Chris.